We love Moody Gardens. However, it isn't really close to the Strand (trolley) and the well known restaurants. You will need to use ride share, taxi or rental car to get to the attractions on the Sea Wall or The Strand. They do have the waterpark right at the hotel, for the kids, big or small. I don't know what time of year you're coming in. Check Google Maps and you will see just how far you are from things.
We also love Hilton and San Luis, but they are usually a lot more pricey.
We just started sailing out of Galveston again recently, so not sure of the hotels we used to stay at.
Sherry